I have a similar problem, adding that it now shakes when idle...but only after a few minutes of driving. It actually now started to turn off while @ slow speeds. A former Hyundai mechanic suggected replacing the Throttle Position Sensor ($50), I will try tomorrow and let you know.
Update:
Well I had a mechanic neighboor look @ it. Said my coils were bad. I replaced them, but the car idled a little rougher. I replaced the Wireset also, idled smoother and I thought all was good. Until 1 day it wouldn't start. Found that if I started up right aways as soon as I put in the key...it started fine. Thought all was good again, so I began running to car harder, and the jerking returned (rarely). Finally replace the TPS with a small 'S' shape screwdriver and notice no change. Not sure what else to change...MAS, spark plugs, belts, hoses?

To both of you, based on your descriptions of the problem, you might want to check the crankshaft position sensor to see if that is the problem. Another possibility is the camshaft sensor as well. Before doing anything it would be a very good idea to get the car's computer read for error codes. If you don't have a reader, you can get them read for free at an Autozone if you happen to have one near you. In my case it was the crankshaft sensor that was keeping my 2000 Hyundai Elantra from starting every now and then. The crankshaft sensor error code was popping up every now and then as well. After doing some research on the net, I was able to locate the sensor. I decided to do a quick verification of the defective part by spraying some electronic component cooler on it that I happened to have lying around. The idea is simple, if an electronic component is bad and not working correctly, it should start to work after it has been chilled. I sprayed the sensor until white frost appeared on the sensor housing and then tried to start my car. Sure enough, my car started right up. If you are interested in getting some electronic component cooler, you should be able to do so at Radio Shack (Cat No. 64-4321). I got mine about 2008, so you will want to verify that they still carry it. One word of caution though, only use this stuff on a cold engine that is at ambient temperature only. If you use this stuff on a hot engine, you run the risk of cracking your engine block. good luck.

You are right. The car stalled out on me on the freeway and wouldn't start. After a few munites I got it to run again, but this time the check engine light came on. I had a friend lend me his code reader and picked up 3 codes, 1 for Mas Air Flow sensore, and 2 for Transmission solenoids. Took it to the dealer and the changed the MAS sensor and Crank Position sensor...and belts and stuff while they were there (not 4 free). Car runs good now.
Wonder if the crank position sensor is defective in these cars? I had it changed also @ 45K mi (Belts and everything too) still under warranty @ the time. Now again it goes bad @ 81K mi.